#include "pseries.h"
#include "utils.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
//////////
// exponential function
static ex exp_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(exp(x))
+ if (is_exactly_a<numeric>(x))
+ return exp(ex_to<numeric>(x));
- return exp(ex_to_numeric(x)); // -> numeric exp(numeric)
+ return exp(x).hold();
}
static ex exp_eval(const ex & x)
return _ex1();
}
// exp(n*Pi*I/2) -> {+1|+I|-1|-I}
- ex TwoExOverPiI=(_ex2()*x)/(Pi*I);
+ const ex TwoExOverPiI=(_ex2()*x)/(Pi*I);
if (TwoExOverPiI.info(info_flags::integer)) {
- numeric z=mod(ex_to_numeric(TwoExOverPiI),_num4());
+ numeric z=mod(ex_to<numeric>(TwoExOverPiI),_num4());
if (z.is_equal(_num0()))
return _ex1();
if (z.is_equal(_num1()))
// exp(float)
if (x.info(info_flags::numeric) && !x.info(info_flags::crational))
- return exp_evalf(x);
+ return exp(ex_to<numeric>(x));
return exp(x).hold();
}
REGISTER_FUNCTION(exp, eval_func(exp_eval).
evalf_func(exp_evalf).
- derivative_func(exp_deriv));
+ derivative_func(exp_deriv).
+ latex_name("\\exp"));
//////////
// natural logarithm
static ex log_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(log(x))
+ if (is_exactly_a<numeric>(x))
+ return log(ex_to<numeric>(x));
- return log(ex_to_numeric(x)); // -> numeric log(numeric)
+ return log(x).hold();
}
static ex log_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
- if (x.is_equal(_ex0())) // log(0) -> infinity
+ if (x.is_zero()) // log(0) -> infinity
throw(pole_error("log_eval(): log(0)",0));
if (x.info(info_flags::real) && x.info(info_flags::negative))
return (log(-x)+I*Pi);
return (Pi*I*_num_1_2());
// log(float)
if (!x.info(info_flags::crational))
- return log_evalf(x);
+ return log(ex_to<numeric>(x));
}
// log(exp(t)) -> t (if -Pi < t.imag() <= Pi):
if (is_ex_the_function(x, exp)) {
ex t = x.op(0);
if (t.info(info_flags::numeric)) {
- numeric nt = ex_to_numeric(t);
+ numeric nt = ex_to<numeric>(t);
if (nt.is_real())
return t;
}
} catch (pole_error) {
must_expand_arg = true;
}
- // or we are at the branch cut anyways
+ // or we are at the branch point anyways
if (arg_pt.is_zero())
must_expand_arg = true;
// Return a plain n*log(x) for the x^n part and series expand the
// other part. Add them together and reexpand again in order to have
// one unnested pseries object. All this also works for negative n.
- const pseries argser = ex_to_pseries(arg.series(rel, order, options));
+ const pseries argser = ex_to<pseries>(arg.series(rel, order, options));
const symbol *s = static_cast<symbol *>(rel.lhs().bp);
const ex point = rel.rhs();
const int n = argser.ldegree(*s);
epvector seq;
- seq.push_back(expair(n*log(*s-point), _ex0()));
+ // construct what we carelessly called the n*log(x) term above
+ ex coeff = argser.coeff(*s, n);
+ // expand the log, but only if coeff is real and > 0, since otherwise
+ // it would make the branch cut run into the wrong direction
+ if (coeff.info(info_flags::positive))
+ seq.push_back(expair(n*log(*s-point)+log(coeff), _ex0()));
+ else
+ seq.push_back(expair(log(coeff*pow(*s-point, n)), _ex0()));
if (!argser.is_terminating() || argser.nops()!=1) {
// in this case n more terms are needed
- ex newarg = ex_to_pseries(arg.series(rel, order+n, options)).shift_exponents(-n).convert_to_poly(true);
- return pseries(rel, seq).add_series(ex_to_pseries(log(newarg).series(rel, order, options)));
+ // (sadly, to generate them, we have to start from the beginning)
+ ex newarg = ex_to<pseries>((arg/coeff).series(rel, order+n, options)).shift_exponents(-n).convert_to_poly(true);
+ return pseries(rel, seq).add_series(ex_to<pseries>(log(newarg).series(rel, order, options)));
} else // it was a monomial
return pseries(rel, seq);
}
if (!(options & series_options::suppress_branchcut) &&
- arg_pt.info(info_flags::negative)) {
+ arg_pt.info(info_flags::negative)) {
// method:
// This is the branch cut: assemble the primitive series manually and
// then add the corresponding complex step function.
const symbol *s = static_cast<symbol *>(rel.lhs().bp);
const ex point = rel.rhs();
const symbol foo;
- ex replarg = series(log(arg), *s==foo, order, false).subs(foo==point);
+ const ex replarg = series(log(arg), *s==foo, order).subs(foo==point);
epvector seq;
seq.push_back(expair(-I*csgn(arg*I)*Pi, _ex0()));
seq.push_back(expair(Order(_ex1()), order));
REGISTER_FUNCTION(log, eval_func(log_eval).
evalf_func(log_evalf).
derivative_func(log_deriv).
- series_func(log_series));
+ series_func(log_series).
+ latex_name("\\ln"));
//////////
// sine (trigonometric function)
static ex sin_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(sin(x))
+ if (is_exactly_a<numeric>(x))
+ return sin(ex_to<numeric>(x));
- return sin(ex_to_numeric(x)); // -> numeric sin(numeric)
+ return sin(x).hold();
}
static ex sin_eval(const ex & x)
{
// sin(n/d*Pi) -> { all known non-nested radicals }
- ex SixtyExOverPi = _ex60()*x/Pi;
+ const ex SixtyExOverPi = _ex60()*x/Pi;
ex sign = _ex1();
if (SixtyExOverPi.info(info_flags::integer)) {
- numeric z = mod(ex_to_numeric(SixtyExOverPi),_num120());
+ numeric z = mod(ex_to<numeric>(SixtyExOverPi),_num120());
if (z>=_num60()) {
// wrap to interval [0, Pi)
z -= _num60();
return sign*_ex1();
}
- if (is_ex_exactly_of_type(x, function)) {
+ if (is_exactly_a<function>(x)) {
ex t = x.op(0);
// sin(asin(x)) -> x
if (is_ex_the_function(x, asin))
// sin(float) -> float
if (x.info(info_flags::numeric) && !x.info(info_flags::crational))
- return sin_evalf(x);
+ return sin(ex_to<numeric>(x));
return sin(x).hold();
}
REGISTER_FUNCTION(sin, eval_func(sin_eval).
evalf_func(sin_evalf).
- derivative_func(sin_deriv));
+ derivative_func(sin_deriv).
+ latex_name("\\sin"));
//////////
// cosine (trigonometric function)
static ex cos_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(cos(x))
+ if (is_exactly_a<numeric>(x))
+ return cos(ex_to<numeric>(x));
- return cos(ex_to_numeric(x)); // -> numeric cos(numeric)
+ return cos(x).hold();
}
static ex cos_eval(const ex & x)
{
// cos(n/d*Pi) -> { all known non-nested radicals }
- ex SixtyExOverPi = _ex60()*x/Pi;
+ const ex SixtyExOverPi = _ex60()*x/Pi;
ex sign = _ex1();
if (SixtyExOverPi.info(info_flags::integer)) {
- numeric z = mod(ex_to_numeric(SixtyExOverPi),_num120());
+ numeric z = mod(ex_to<numeric>(SixtyExOverPi),_num120());
if (z>=_num60()) {
// wrap to interval [0, Pi)
z = _num120()-z;
return sign*_ex0();
}
- if (is_ex_exactly_of_type(x, function)) {
+ if (is_exactly_a<function>(x)) {
ex t = x.op(0);
// cos(acos(x)) -> x
if (is_ex_the_function(x, acos))
// cos(float) -> float
if (x.info(info_flags::numeric) && !x.info(info_flags::crational))
- return cos_evalf(x);
+ return cos(ex_to<numeric>(x));
return cos(x).hold();
}
REGISTER_FUNCTION(cos, eval_func(cos_eval).
evalf_func(cos_evalf).
- derivative_func(cos_deriv));
+ derivative_func(cos_deriv).
+ latex_name("\\cos"));
//////////
// tangent (trigonometric function)
static ex tan_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(tan(x)) // -> numeric tan(numeric)
+ if (is_exactly_a<numeric>(x))
+ return tan(ex_to<numeric>(x));
- return tan(ex_to_numeric(x));
+ return tan(x).hold();
}
static ex tan_eval(const ex & x)
{
// tan(n/d*Pi) -> { all known non-nested radicals }
- ex SixtyExOverPi = _ex60()*x/Pi;
+ const ex SixtyExOverPi = _ex60()*x/Pi;
ex sign = _ex1();
if (SixtyExOverPi.info(info_flags::integer)) {
- numeric z = mod(ex_to_numeric(SixtyExOverPi),_num60());
+ numeric z = mod(ex_to<numeric>(SixtyExOverPi),_num60());
if (z>=_num60()) {
// wrap to interval [0, Pi)
z -= _num60();
throw (pole_error("tan_eval(): simple pole",1));
}
- if (is_ex_exactly_of_type(x, function)) {
+ if (is_exactly_a<function>(x)) {
ex t = x.op(0);
// tan(atan(x)) -> x
if (is_ex_the_function(x, atan))
// tan(float) -> float
if (x.info(info_flags::numeric) && !x.info(info_flags::crational)) {
- return tan_evalf(x);
+ return tan(ex_to<numeric>(x));
}
return tan(x).hold();
REGISTER_FUNCTION(tan, eval_func(tan_eval).
evalf_func(tan_evalf).
derivative_func(tan_deriv).
- series_func(tan_series));
+ series_func(tan_series).
+ latex_name("\\tan"));
//////////
// inverse sine (arc sine)
static ex asin_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(asin(x))
+ if (is_exactly_a<numeric>(x))
+ return asin(ex_to<numeric>(x));
- return asin(ex_to_numeric(x)); // -> numeric asin(numeric)
+ return asin(x).hold();
}
static ex asin_eval(const ex & x)
return _num_1_2()*Pi;
// asin(float) -> float
if (!x.info(info_flags::crational))
- return asin_evalf(x);
+ return asin(ex_to<numeric>(x));
}
return asin(x).hold();
REGISTER_FUNCTION(asin, eval_func(asin_eval).
evalf_func(asin_evalf).
- derivative_func(asin_deriv));
+ derivative_func(asin_deriv).
+ latex_name("\\arcsin"));
//////////
// inverse cosine (arc cosine)
static ex acos_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(acos(x))
+ if (is_exactly_a<numeric>(x))
+ return acos(ex_to<numeric>(x));
- return acos(ex_to_numeric(x)); // -> numeric acos(numeric)
+ return acos(x).hold();
}
static ex acos_eval(const ex & x)
return Pi;
// acos(float) -> float
if (!x.info(info_flags::crational))
- return acos_evalf(x);
+ return acos(ex_to<numeric>(x));
}
return acos(x).hold();
REGISTER_FUNCTION(acos, eval_func(acos_eval).
evalf_func(acos_evalf).
- derivative_func(acos_deriv));
+ derivative_func(acos_deriv).
+ latex_name("\\arccos"));
//////////
// inverse tangent (arc tangent)
static ex atan_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(atan(x))
+ if (is_exactly_a<numeric>(x))
+ return atan(ex_to<numeric>(x));
- return atan(ex_to_numeric(x)); // -> numeric atan(numeric)
+ return atan(x).hold();
}
static ex atan_eval(const ex & x)
{
if (x.info(info_flags::numeric)) {
// atan(0) -> 0
- if (x.is_equal(_ex0()))
+ if (x.is_zero())
return _ex0();
// atan(1) -> Pi/4
if (x.is_equal(_ex1()))
throw (pole_error("atan_eval(): logarithmic pole",0));
// atan(float) -> float
if (!x.info(info_flags::crational))
- return atan_evalf(x);
+ return atan(ex_to<numeric>(x));
}
return atan(x).hold();
return power(_ex1()+power(x,_ex2()), _ex_1());
}
-static ex atan_series(const ex &x,
+static ex atan_series(const ex &arg,
const relational &rel,
int order,
unsigned options)
// one running from -I down the imaginary axis. The points I and -I are
// poles.
// On the branch cuts and the poles series expand
- // log((1+I*x)/(1-I*x))/(2*I)
+ // (log(1+I*x)-log(1-I*x))/(2*I)
// instead.
- // (The constant term on the cut itself could be made simpler.)
- const ex x_pt = x.subs(rel);
- if (!(I*x_pt).info(info_flags::real))
+ const ex arg_pt = arg.subs(rel);
+ if (!(I*arg_pt).info(info_flags::real))
throw do_taylor(); // Re(x) != 0
- if ((I*x_pt).info(info_flags::real) && abs(I*x_pt)<_ex1())
+ if ((I*arg_pt).info(info_flags::real) && abs(I*arg_pt)<_ex1())
throw do_taylor(); // Re(x) == 0, but abs(x)<1
- // if we got here we have to care for cuts and poles
- return (log((1+I*x)/(1-I*x))/(2*I)).series(rel, order, options);
+ // care for the poles, using the defining formula for atan()...
+ if (arg_pt.is_equal(I) || arg_pt.is_equal(-I))
+ return ((log(1+I*arg)-log(1-I*arg))/(2*I)).series(rel, order, options);
+ if (!(options & series_options::suppress_branchcut)) {
+ // method:
+ // This is the branch cut: assemble the primitive series manually and
+ // then add the corresponding complex step function.
+ const symbol *s = static_cast<symbol *>(rel.lhs().bp);
+ const ex point = rel.rhs();
+ const symbol foo;
+ const ex replarg = series(atan(arg), *s==foo, order).subs(foo==point);
+ ex Order0correction = replarg.op(0)+csgn(arg)*Pi*_ex_1_2();
+ if ((I*arg_pt)<_ex0())
+ Order0correction += log((I*arg_pt+_ex_1())/(I*arg_pt+_ex1()))*I*_ex_1_2();
+ else
+ Order0correction += log((I*arg_pt+_ex1())/(I*arg_pt+_ex_1()))*I*_ex1_2();
+ epvector seq;
+ seq.push_back(expair(Order0correction, _ex0()));
+ seq.push_back(expair(Order(_ex1()), order));
+ return series(replarg - pseries(rel, seq), rel, order);
+ }
+ throw do_taylor();
}
REGISTER_FUNCTION(atan, eval_func(atan_eval).
evalf_func(atan_evalf).
derivative_func(atan_deriv).
- series_func(atan_series));
+ series_func(atan_series).
+ latex_name("\\arctan"));
//////////
// inverse tangent (atan2(y,x))
//////////
-static ex atan2_evalf(const ex & y, const ex & x)
+static ex atan2_evalf(const ex &y, const ex &x)
{
- BEGIN_TYPECHECK
- TYPECHECK(y,numeric)
- TYPECHECK(x,numeric)
- END_TYPECHECK(atan2(y,x))
+ if (is_exactly_a<numeric>(y) && is_exactly_a<numeric>(x))
+ return atan2(ex_to<numeric>(y), ex_to<numeric>(x));
- return atan(ex_to_numeric(y),ex_to_numeric(x)); // -> numeric atan(numeric)
+ return atan2(y, x).hold();
}
static ex atan2_eval(const ex & y, const ex & x)
static ex sinh_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(sinh(x))
+ if (is_exactly_a<numeric>(x))
+ return sinh(ex_to<numeric>(x));
- return sinh(ex_to_numeric(x)); // -> numeric sinh(numeric)
+ return sinh(x).hold();
}
static ex sinh_eval(const ex & x)
if (x.is_zero()) // sinh(0) -> 0
return _ex0();
if (!x.info(info_flags::crational)) // sinh(float) -> float
- return sinh_evalf(x);
+ return sinh(ex_to<numeric>(x));
}
if ((x/Pi).info(info_flags::numeric) &&
- ex_to_numeric(x/Pi).real().is_zero()) // sinh(I*x) -> I*sin(x)
+ ex_to<numeric>(x/Pi).real().is_zero()) // sinh(I*x) -> I*sin(x)
return I*sin(x/I);
- if (is_ex_exactly_of_type(x, function)) {
+ if (is_exactly_a<function>(x)) {
ex t = x.op(0);
// sinh(asinh(x)) -> x
if (is_ex_the_function(x, asinh))
REGISTER_FUNCTION(sinh, eval_func(sinh_eval).
evalf_func(sinh_evalf).
- derivative_func(sinh_deriv));
+ derivative_func(sinh_deriv).
+ latex_name("\\sinh"));
//////////
// hyperbolic cosine (trigonometric function)
static ex cosh_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(cosh(x))
+ if (is_exactly_a<numeric>(x))
+ return cosh(ex_to<numeric>(x));
- return cosh(ex_to_numeric(x)); // -> numeric cosh(numeric)
+ return cosh(x).hold();
}
static ex cosh_eval(const ex & x)
if (x.is_zero()) // cosh(0) -> 1
return _ex1();
if (!x.info(info_flags::crational)) // cosh(float) -> float
- return cosh_evalf(x);
+ return cosh(ex_to<numeric>(x));
}
if ((x/Pi).info(info_flags::numeric) &&
- ex_to_numeric(x/Pi).real().is_zero()) // cosh(I*x) -> cos(x)
+ ex_to<numeric>(x/Pi).real().is_zero()) // cosh(I*x) -> cos(x)
return cos(x/I);
- if (is_ex_exactly_of_type(x, function)) {
+ if (is_exactly_a<function>(x)) {
ex t = x.op(0);
// cosh(acosh(x)) -> x
if (is_ex_the_function(x, acosh))
REGISTER_FUNCTION(cosh, eval_func(cosh_eval).
evalf_func(cosh_evalf).
- derivative_func(cosh_deriv));
-
+ derivative_func(cosh_deriv).
+ latex_name("\\cosh"));
//////////
// hyperbolic tangent (trigonometric function)
static ex tanh_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(tanh(x))
+ if (is_exactly_a<numeric>(x))
+ return tanh(ex_to<numeric>(x));
- return tanh(ex_to_numeric(x)); // -> numeric tanh(numeric)
+ return tanh(x).hold();
}
static ex tanh_eval(const ex & x)
if (x.is_zero()) // tanh(0) -> 0
return _ex0();
if (!x.info(info_flags::crational)) // tanh(float) -> float
- return tanh_evalf(x);
+ return tanh(ex_to<numeric>(x));
}
if ((x/Pi).info(info_flags::numeric) &&
- ex_to_numeric(x/Pi).real().is_zero()) // tanh(I*x) -> I*tan(x);
+ ex_to<numeric>(x/Pi).real().is_zero()) // tanh(I*x) -> I*tan(x);
return I*tan(x/I);
- if (is_ex_exactly_of_type(x, function)) {
+ if (is_exactly_a<function>(x)) {
ex t = x.op(0);
// tanh(atanh(x)) -> x
if (is_ex_the_function(x, atanh))
REGISTER_FUNCTION(tanh, eval_func(tanh_eval).
evalf_func(tanh_evalf).
derivative_func(tanh_deriv).
- series_func(tanh_series));
+ series_func(tanh_series).
+ latex_name("\\tanh"));
//////////
// inverse hyperbolic sine (trigonometric function)
static ex asinh_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(asinh(x))
+ if (is_exactly_a<numeric>(x))
+ return asinh(ex_to<numeric>(x));
- return asinh(ex_to_numeric(x)); // -> numeric asinh(numeric)
+ return asinh(x).hold();
}
static ex asinh_eval(const ex & x)
return _ex0();
// asinh(float) -> float
if (!x.info(info_flags::crational))
- return asinh_evalf(x);
+ return asinh(ex_to<numeric>(x));
}
return asinh(x).hold();
static ex acosh_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(acosh(x))
+ if (is_exactly_a<numeric>(x))
+ return acosh(ex_to<numeric>(x));
- return acosh(ex_to_numeric(x)); // -> numeric acosh(numeric)
+ return acosh(x).hold();
}
static ex acosh_eval(const ex & x)
return Pi*I;
// acosh(float) -> float
if (!x.info(info_flags::crational))
- return acosh_evalf(x);
+ return acosh(ex_to<numeric>(x));
}
return acosh(x).hold();
static ex atanh_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(atanh(x))
+ if (is_exactly_a<numeric>(x))
+ return atanh(ex_to<numeric>(x));
- return atanh(ex_to_numeric(x)); // -> numeric atanh(numeric)
+ return atanh(x).hold();
}
static ex atanh_eval(const ex & x)
throw (pole_error("atanh_eval(): logarithmic pole",0));
// atanh(float) -> float
if (!x.info(info_flags::crational))
- return atanh_evalf(x);
+ return atanh(ex_to<numeric>(x));
}
return atanh(x).hold();
return power(_ex1()-power(x,_ex2()),_ex_1());
}
-static ex atanh_series(const ex &x,
+static ex atanh_series(const ex &arg,
const relational &rel,
int order,
unsigned options)
{
GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol));
// method:
- // Taylor series where there is no pole or cut falls back to atan_deriv.
+ // Taylor series where there is no pole or cut falls back to atanh_deriv.
// There are two branch cuts, one runnig from 1 up the real axis and one
// one running from -1 down the real axis. The points 1 and -1 are poles
// On the branch cuts and the poles series expand
- // log((1+x)/(1-x))/(2*I)
+ // (log(1+x)-log(1-x))/2
// instead.
- // (The constant term on the cut itself could be made simpler.)
- const ex x_pt = x.subs(rel);
- if (!(x_pt).info(info_flags::real))
+ const ex arg_pt = arg.subs(rel);
+ if (!(arg_pt).info(info_flags::real))
throw do_taylor(); // Im(x) != 0
- if ((x_pt).info(info_flags::real) && abs(x_pt)<_ex1())
+ if ((arg_pt).info(info_flags::real) && abs(arg_pt)<_ex1())
throw do_taylor(); // Im(x) == 0, but abs(x)<1
- // if we got here we have to care for cuts and poles
- return (log((1+x)/(1-x))/2).series(rel, order, options);
+ // care for the poles, using the defining formula for atanh()...
+ if (arg_pt.is_equal(_ex1()) || arg_pt.is_equal(_ex_1()))
+ return ((log(_ex1()+arg)-log(_ex1()-arg))*_ex1_2()).series(rel, order, options);
+ // ...and the branch cuts (the discontinuity at the cut being just I*Pi)
+ if (!(options & series_options::suppress_branchcut)) {
+ // method:
+ // This is the branch cut: assemble the primitive series manually and
+ // then add the corresponding complex step function.
+ const symbol *s = static_cast<symbol *>(rel.lhs().bp);
+ const ex point = rel.rhs();
+ const symbol foo;
+ const ex replarg = series(atanh(arg), *s==foo, order).subs(foo==point);
+ ex Order0correction = replarg.op(0)+csgn(I*arg)*Pi*I*_ex1_2();
+ if (arg_pt<_ex0())
+ Order0correction += log((arg_pt+_ex_1())/(arg_pt+_ex1()))*_ex1_2();
+ else
+ Order0correction += log((arg_pt+_ex1())/(arg_pt+_ex_1()))*_ex_1_2();
+ epvector seq;
+ seq.push_back(expair(Order0correction, _ex0()));
+ seq.push_back(expair(Order(_ex1()), order));
+ return series(replarg - pseries(rel, seq), rel, order);
+ }
+ throw do_taylor();
}
REGISTER_FUNCTION(atanh, eval_func(atanh_eval).
series_func(atanh_series));
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
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